The term "AC circuits" covers a lot of ground and a lot of different types of circuits that do a lot of different kinds of things. Also, a lot depends on how these unspecified rectifiers are used with regard to these unspecified AC circuits.

The question is written as explain the potential effects that the use of rectifiers has on AC circuits and supplies: and considerations required when designing electrical circuits when rectifiers are installed.

Here are some considerations when using rectifiers to generate DC from AC:
Half-wave or full-wave.
Peak current from AC supply drawn by the diodes (which requires derating of a transformer supplying the AC).
DC ripple voltage versus output current (size of filter capacitor).
Diode voltage and current rating.

Also for the most part capacitive smoothing is not usually required with DC motor's and other inductive devices.
If such as PWM control is used, then a smoothed supply is desirable.
There are also SCR bridge and Triac control of DC motor where capacitive smoothing is not required.
Max.